# need solution

1.A triangle is formed by the line connecting the midpoints of two adjacent sides of a rectangle. Find the area of this triangle if the area of the rectangle is 8 square units. why ?

2. when freezing, water increases its volume by 1/11. By what part of its volume will ice decrease when it melts and turns back into water? why?

3, in a children's game, you count from 1 to 100 and clap every time that you find either a multiple of 3 or a number ending with 3. How may times are you suppose to clap ? why ?

### 4 個解答

- DaSaGwaLv 75 年前最佳解答
1.

If You divid the rectangle at middle point of each side, you will get 4 rectangle and each has area of 2. Then divide one of the 4 smaller rectangle, you will get the triangle described by the question, and its area is equal to 1.

2.

The volume of the water before and after freezing is the same. Let's assume the volume is equal to 1.

the volume after freezing = 1+ 1/11 = 12/11

since after the ice melt, the volume will go back to 1, hence 12/11 - (12/11)(1/12) = 1

volume will ice decrease = 1/12

3.

number ending with 3

3, 13, 23, ... 93 ==> 10 numbers

a multiple of 3

3, 33, 63, 93 ==> 4 numbers (however, these 4 appear in number ending with 3)

How may times are you suppose to clap ? 10

2014-10-24 21:40:54 補充：

Sorry, I miscount 30, so

a multiple of 3

3, 30, 33, 63, 93 ==> 5 numbers (however, these 4 appear in number ending with 3)

How may times are you suppose to clap ? 11

2014-10-24 21:42:52 補充：

volume will ice decrease = 1/12

==> volume ice will decrease = 1/12

2014-10-25 02:36:04 補充：

If the result of the multiplication doesn't need to have digit 3 in it, then master DarkHelmet is correct. If the result needs to have digit 3, then mine is correct.

2014-10-25 02:37:33 補充：

The one I have seen before, is not for digit 3, but digit 9. It counts only the result with digit 9.

2014-10-25 06:16:23 補充：

Well, I certainly know what "multiple" means.

I think, I have solved the problem for a multiple of 3 "with digit 3".

2014-10-25 06:18:28 補充：

Look like I think too much, shall have taken "a multiple of 3" as is, not to connect with "digit 3".

2014-10-27 08:50:23 補充：

the third question isn't right the right answer is 39 but i don't know why .....

Well, if the answer is 39, then master DarkHelmet's comment in #001 is the reason behind 39.

2014-10-27 08:51:48 補充：

It means, I have read the question wrong for this portion: a multiple of 3.

I took it as not only a multiple of three, but also the result needs to have digit 3 in it.

2014-10-27 09:02:13 補充：

Chinese said, "Drawing a snake with legs". It is why I didn't get the right answer. I think too much, and make the question more difficult (have more restriction) than the statement is.

2014-10-28 10:02:25 補充：

The decrease amount is based upon the ice volume, not the water volume. Since when water becomes ice, its volume has increased, that is why the decrease amount is less.

- 5 年前
Why the answer of the second question is 1/12? Why isn't it the original increased part of 1/11?

- Dark HelmetLv 75 年前
There are 33 multiples of 3 (3, 6, 9, 12..........., 99)

There are 10 numbers ending with 3 (3, 13, 23, 33, ......93) , of which 4 numbers are also multiples of 3 (3, 33, 63, 93)

Therefore the answer is 33+10-4=39

2014-10-25 03:50:16 補充：

Read the question: either a multiple of 3 or ending in 3.

a multiple is a number by which it can be divided without a remainder.

2014-10-25 18:42:51 補充：

RE: Look like I think too much (No, not enough.)

光知道“帶粉內尋”顯然不能幫你正確地從1～100 選出3 的倍數. 你需要閱讀英語寫的書，來建立起自己和英文之間親密的“飛靈”. 這樣你就不會有任何困了解句子的“康泰克斯”

2014-10-28 07:50:39 補充：

Chinese also said, "The more you trace it, the blacker it gets."